The present invention relates to the design of optical elements, in general, and to a method for designing optical elements using wavefront calculations, in particular.
Most of the designs for progressive (multifocal) ophthalmic lenses are based mainly on the geometrical shape of one or more of the lens surfaces, as described, for example in U.S. Pat. No. 3,687,528 to Maitenaz. The geometrical properties, however, are only indirectly related to the lens"" actual optical performance. For example, the curvature of any of the lens surfaces is only approximately related to the lens optical power. In some cases, for example U.S. patent application Ser. No. 09/262,341 to Katzman et al., entitled xe2x80x9cMETHOD FOR THE DESIGN OF MULTIFOCAL OPTICAL ELEMENTSxe2x80x9d, filed Mar. 4, 1999, the design is examined for its actual optical performance, and parameters of the design process can be adjusted in response to the optical performance, but this makes the design process indirect and time-consuming.
Another typical approach in lens design is to use software means to trace a large number of rays through the lens and to deduce from the incident and refracted rays the classical aberrations of the lens. The surfaces of the lens are represented in terms of a fixed number of basic surfaces such as spheres, aspherics, torics and cylindrical surfaces. The ray tracing of a large number of rays requires a considerable computational effort, and the limited family of surfaces in which one optimizes the lens performance greatly restricts the optimization capabilities.
Several methods were proposed to overcome the undesirable constraint of a limited family of optical surfaces. U.S. Pat. No. 4,613,217 to Fueter et al. proposes to represent an optical surface by splines. U.S. Pat. No. 5,886,766 to Kaga et al. similarly proposes a progressive ophthalmic lens consisting of three portions, at least one of which is divided into smaller pieces that are connected together by requiring that the surface is at least twice continuously differentiable along the interfaces joining two pieces. The spline representation, while offering an advantage over the limited class of surfaces mentioned above, has several drawbacks: the strict smoothness requirements along boundaries limits the space of parameters for the optimization process, the restriction to rectangular pieces, and thus to rectangular domains, limits the flexibility of the design, and it is not fully natural to prescribe boundary conditions on the lens surfaces and their slopes. U.S. patent application Ser. No. 09/262,341 to Katzman et al. describes a finite element method for the surface representation. The finite elements are patches of arbitrary polygonal shape, thus yielding flexible designs. The method of U.S. patent application Ser. No. 09/262,341 to Katzman et al. requires less differentiability along the lines joining the patches than that of U.S. Pat. No. 5,886,766 to Kaga et al.
The common practice in the ophthalmic industry is to design and manufacture semi-finished lenses. The lens is manufactured with one surface that is given, for example a spherical or toric surface, and one surface that is designed. The given surface is later processed to meet the specific prescription of the client. Consequently most designs are limited in that they take into account only one surface of the lens, assuming, in general, a given spherical or toric other surface. Furthermore, the capability of improving the lens performance by designing both surfaces is not utilized. Recent technological developments enable better control of the manufacturing of both surfaces of ophthalmic lenses. Indeed, U.S. Pat. No. 5,771,089 to Barth, U.S. Pat. No. 5,784,144 to Kelch and U.S. patent application Ser. No. 09/262,341 to Katzman et al. propose designs in which both the front and back surfaces of the lens have flexible shapes. Further technological developments enable manufacturing of multi-surface ophthalmic lenses. U.S. patent application Ser. No. 09/262,341 to Katzman et al. proposes designs in which several of the surfaces have flexible shapes.
In the design of multifocal ophthalmic lens, one usually selects the front (far from eye) surface to be progressive, while the back (close to eye) surface is either spherical or toric, where a toric surface might be needed to correct astigmatism. U.S. Pat. No. 2,878,721 to Kanolt and U.S. Pat. No. 6,019,470 to Mukaiyama et al. disclose ophthalmic lenses in which the back surface is a composition of a progressive surface and a toric surface. This composite design has a drawback that each of the two surfaces (toric and progressive) is designed separately, and thus the optical behavior of one of the surfaces may conflict with the optical behavior of the other. It is therefore beneficial to develop a method for designing a lens consisting of integral surfaces rather than composite surfaces. Such a method could then simultaneously consider all desired optical behavior.
The actual performance of an ophthalmic lens depends not just on the lens itself, but on the full eye-plus-lens system. This becomes particularly important, for example, when the lens user suffers from astigmatism and/or presbyopia. Astigmatism is a condition in which the eye focuses differently in different directions. Presbyopia is a condition in which the eye loses some of its ability to accommodate, i.e. to focus sharply at nearby objects. The curvature of the lens of the eye changes as the eye focuses on objects at different distances from the eye. As people age, their eyes become less elastic and therefore can change the curvature of the lens only to a certain degree.
The article by J. Loos, Ph. Slusallek and H.-P. Seidel, entitled xe2x80x9cUsing Wavefront Tracing for the Visualization and Optimization of Progressive Lensesxe2x80x9d, Computer Graphics Forum, vol. 17, no. 3, 1998, pp. 255-264, discusses the possibility of accounting for the eye structure in the design process of progressive lenses. However, Loos et al. do not require a full analysis of astigmatism and presbyopia since they assume a spherical or toroidal back surface and optimize only the front surface of the progressive lens.
An important characteristic of a lens is its prism. Prism measures the change in the direction of light rays as they are refracted by the lens. Essentially every lens has some level of prism. Sometimes a lens is processed in order to induce some desired prism for a variety of purposes. However, design methods taking prism into account are not known.
There is provided in accordance with an embodiment of the present invention a method for designing at least one surface of an optical element. For each particular surface, a representation is created with a set of discrete points. Then for each discrete point in the set, nearest neighbor points from the set are selected, the particular surface is approximated in a vicinity of the discrete point by a polynomial of a predetermined order in two variables of the particular surface, and the coefficients of the polynomial are determined according to the selected nearest neighbor points without requiring continuity between polynomials for neighboring discrete points.
There is also provided in accordance with an embodiment of the present invention a method for designing at least one surface of an optical element. The method includes the steps of representing the at least one surface using the method of unconstrained patches, choosing a function in parameters of the at least one surface, and optimizing the function with respect to the parameters.
There is also provided in accordance with an embodiment of the present invention a method for designing at least one surface of an ophthalmic lens. The method includes the steps of representing the at least one surface with parameters, choosing a function in the parameters, and optimizing the function with respect to the parameters.
Preferably, the ophthalmic lens is a multifocal progressive lens.
Preferably, the function includes a term involving the difference between the astigmatism induced by the ophthalmic lens and a predetermined astigmatism distribution. The predetermined astigmatism distribution describes different astigmatism than that required by a prescription for the ophthalmic lens.
Preferably, the function includes a term involving a power other than 2 of the astigmatism induced by the ophthalmic lens.
Preferably, the function includes a term involving the difference between the prism induced by the ophthalmic lens and a predetermined prism distribution.
Preferably, the function includes a term involving the difference between the gradient of a characteristic and the gradient of a predetermined characteristic distribution, where the characteristic is selected from a group including: power, astigmatism, and prism.
Preferably, the function includes the square of the difference between the power induced by the ophthalmic lens and a predetermined power distribution and other terms related to the power induced by the ophthalmic lens. The other terms related to the power induced by the ophthalmic lens include terms of the form |P(l,m)xe2x88x92Pv(l,m)|xcex2 for at least one value of xcex2 other than 2, where P(l,m) denotes the power induced by the optical element, Pv(l,m) denotes the predetermined power distribution, and (l,m) parameterize the surfaces of the ophthalmic lens.
Preferably, the function includes a term related to the thickness of the ophthalmic lens.
There is also provided in accordance with an embodiment of the present invention a method for designing at least one surface of a multifocal optical element. The method includes the step of concurrently considering in a design of the at least one surface both toric and progressive portions of a prescription for the multifocal optical element.
There is also provided in accordance with an embodiment of the present invention a method for designing a surface of an optical element. The method includes the steps of prescribing initial wavefronts, selecting an initial representation of the surface, the representation including parameters, and precomputing eikonal functions between points in the vicinity of the initial representation and points in the vicinity of the initial wavefronts. When optimizing a cost function dependent upon the parameters, a refracted wavefront for each of the initial wavefronts is calculated from the precomputed eikonal functions.
Moreover, the step of optimizing includes the step of analytically computing derivatives of the cost function using the precomputed eikonal functions.
Furthermore, if during the step of optimizing, a current representation of the surface varies too much from the initial representation, then eikonal functions between points in the vicinity of the current representation and points in the vicinity of the initial wavefronts are computed.
There is provided in accordance with an embodiment of the present invention a method for designing a surface of an optical element. The method includes the steps of prescribing initial wavefronts, selecting an initial parameterized representation of the surface, choosing a function in the parameters, and optimizing the function with respect to the parameters. The step of optimizing includes the steps of calculating a refracted wavefront for each of the initial wavefronts and analytically computing derivatives of the function.
There is provided in accordance with an embodiment of the present invention a method for designing at least one surface of an ophthalmic lens. The method includes the steps of representing the at least one surface by parameters, choosing an astigmatism distribution and an astigmatism direction distribution, choosing a function in the parameters and optimizing the function with respect to the parameters. The function includes a term involving the astigmatism distribution, the astigmatism direction distribution and the astigmatism induced by the ophthalmic lens.
Preferably, the ophthalmic lens is a multifocal progressive lens.
Preferably, the astigmatism distribution and the astigmatism direction distribution are determined from an eyeglass prescription.
Preferably, the term is of the form       ∑          l      ,      m        ⁢                    w        1            ⁢              (                  l          ,          m                )              ⁢                  "LeftBracketingBar"                                                                              (                                                                                    α                        11                                            ⁢                                              (                                                  l                          ,                          m                                                )                                                              -                                                                  α                        22                                            ⁢                                              (                                                  l                          ,                          m                                                )                                                                              )                                2                            -                                                C                                      V                    ,                    1                                    2                                ⁡                                  (                                      l                    ,                    m                                    )                                            +                                                                    w                    2                                    ⁡                                      (                                          l                      ,                      m                                        )                                                  ⁢                                                      α                    12                    2                                    ⁡                                      (                                          l                      ,                      m                                        )                                                                                -                                    C                              V                ,                2                                      ⁢                          (                              l                ,                m                            )                                      "RightBracketingBar"            β      
where (l,m) index the parameters for the at least one surface, Cv,1 is the astigmatism distribution, Cv,2 is a second astigmatism distribution, xcex111, xcex112 and xcex122 are the coefficients in a quadratic expansion of a wavefront refracted by the lens in a coordinate system chosen for each (l,m) in accordance with the astigmatism direction distribution, w1 and w2 are weight distributions and xcex2 is an exponent.